Question

How do you find the sum of `Sigma (k+1)^2(k-3)` where k is [2,5]?

Answer 1

`sum_(k=2)^5(k+1)^2(k-3)`

With so few terms, since we're only adding `4`, it's easy to just plug in all `k` values from `k=2` to `k=5` and add them:

`=(2+1)^2(2-3)+(3+1)^2(3-3)+(4+1)^2(4-3)+(5+1)^2(5-3)`

`=9(-1)+16(0)+25(1)+36(2)`

`=color(blue)88`